The league announced Friday that Hill, a Jersey City native, had been suspended for the first six games of the season for violating the NFL substance-abuse policy.

It was Hill’s third league drug ban in three years since the Giants signed him as an undrafted free agent out of Florida.

Tom Coughlin hinted at the Giants’ disgust with Hill last Thursday, when he told reporters after a voluntary offseason practice — which Hill participated in while appealing the suspension — that uncertainty surrounding the safety “is and it will be [a difficult situation].”

The Giants also made it clear Hill was at least in Coughlin’s doghouse when he worked with the second- and third-team during Thursday’s practice behind veterans Stevie Brown and Quintin Demps.

Releasing Hill, 24, is a risk only because he is one of the NFL’s most promising young safeties when he isn’t struggling with personal demons.

Hill showed that last season, recording two interceptions, two forced fumbles and 60 tackles in just 12 games after missing the first four games because of a league ban.

Hill’s best moment as a Giant last season came in a Week 16 victory over the Lions, when he intercepted a Matthew Stafford pass and returned it 38 yards for a touchdown in the fourth quarter. Hill’s big play sent the game into overtime, and the Giants pulled off a 23-20 win that eliminated Detroit from playoff contention.

Hill’s current suspension — his second for violating the substance-abuse policy because of a positive marijuana test — was upheld after an arbitrator turned down Hill’s reported claim that he didn’t inhale himself but came up positive due to second-hand smoke.

Hill’s first league ban, during his rookie season in 2012, was also because of a positive marijuana test. His suspension last year was for violating the NFL’s policy on performance-enhancing drugs, an incident that Hill claimed resulted from his use of Adderall to treat attention-deficit disorder.

Because of his immense talent (the website Pro Football Focus ranked him the second-best safety in football last season), Hill isn’t expected to stay unemployed for long. Several teams could use help at safety, including the Jets and the NFC East-rival Eagles and Redskins, and are thought to be willing to give Hill another chance.